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Diffstat (limited to 'media/ffvpx/libavutil/mathematics.c')
| -rw-r--r-- | media/ffvpx/libavutil/mathematics.c | 319 |
1 files changed, 319 insertions, 0 deletions
diff --git a/media/ffvpx/libavutil/mathematics.c b/media/ffvpx/libavutil/mathematics.c new file mode 100644 index 0000000000..61aeb7c029 --- /dev/null +++ b/media/ffvpx/libavutil/mathematics.c @@ -0,0 +1,319 @@ +/* + * Copyright (c) 2005-2012 Michael Niedermayer <michaelni@gmx.at> + * + * This file is part of FFmpeg. + * + * FFmpeg is free software; you can redistribute it and/or + * modify it under the terms of the GNU Lesser General Public + * License as published by the Free Software Foundation; either + * version 2.1 of the License, or (at your option) any later version. + * + * FFmpeg is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public + * License along with FFmpeg; if not, write to the Free Software + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA + */ + +/** + * @file + * miscellaneous math routines and tables + */ + +#include <stdint.h> +#include <limits.h> + +#include "avutil.h" +#include "mathematics.h" +#include "libavutil/intmath.h" +#include "libavutil/common.h" +#include "avassert.h" + +/* Stein's binary GCD algorithm: + * https://en.wikipedia.org/wiki/Binary_GCD_algorithm */ +int64_t av_gcd(int64_t a, int64_t b) { + int za, zb, k; + int64_t u, v; + if (a == 0) + return b; + if (b == 0) + return a; + za = ff_ctzll(a); + zb = ff_ctzll(b); + k = FFMIN(za, zb); + u = llabs(a >> za); + v = llabs(b >> zb); + while (u != v) { + if (u > v) + FFSWAP(int64_t, v, u); + v -= u; + v >>= ff_ctzll(v); + } + return (uint64_t)u << k; +} + +int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd) +{ + int64_t r = 0; + av_assert2(c > 0); + av_assert2(b >=0); + av_assert2((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4); + + if (c <= 0 || b < 0 || !((unsigned)(rnd&~AV_ROUND_PASS_MINMAX)<=5 && (rnd&~AV_ROUND_PASS_MINMAX)!=4)) + return INT64_MIN; + + if (rnd & AV_ROUND_PASS_MINMAX) { + if (a == INT64_MIN || a == INT64_MAX) + return a; + rnd -= AV_ROUND_PASS_MINMAX; + } + + if (a < 0) + return -(uint64_t)av_rescale_rnd(-FFMAX(a, -INT64_MAX), b, c, rnd ^ ((rnd >> 1) & 1)); + + if (rnd == AV_ROUND_NEAR_INF) + r = c / 2; + else if (rnd & 1) + r = c - 1; + + if (b <= INT_MAX && c <= INT_MAX) { + if (a <= INT_MAX) + return (a * b + r) / c; + else { + int64_t ad = a / c; + int64_t a2 = (a % c * b + r) / c; + if (ad >= INT32_MAX && b && ad > (INT64_MAX - a2) / b) + return INT64_MIN; + return ad * b + a2; + } + } else { +#if 1 + uint64_t a0 = a & 0xFFFFFFFF; + uint64_t a1 = a >> 32; + uint64_t b0 = b & 0xFFFFFFFF; + uint64_t b1 = b >> 32; + uint64_t t1 = a0 * b1 + a1 * b0; + uint64_t t1a = t1 << 32; + int i; + + a0 = a0 * b0 + t1a; + a1 = a1 * b1 + (t1 >> 32) + (a0 < t1a); + a0 += r; + a1 += a0 < r; + + for (i = 63; i >= 0; i--) { + a1 += a1 + ((a0 >> i) & 1); + t1 += t1; + if (c <= a1) { + a1 -= c; + t1++; + } + } + if (t1 > INT64_MAX) + return INT64_MIN; + return t1; +#else + /* reference code doing (a*b + r) / c, requires libavutil/integer.h */ + AVInteger ai; + ai = av_mul_i(av_int2i(a), av_int2i(b)); + ai = av_add_i(ai, av_int2i(r)); + + return av_i2int(av_div_i(ai, av_int2i(c))); +#endif + } +} + +int64_t av_rescale(int64_t a, int64_t b, int64_t c) +{ + return av_rescale_rnd(a, b, c, AV_ROUND_NEAR_INF); +} + +int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq, + enum AVRounding rnd) +{ + int64_t b = bq.num * (int64_t)cq.den; + int64_t c = cq.num * (int64_t)bq.den; + return av_rescale_rnd(a, b, c, rnd); +} + +int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) +{ + return av_rescale_q_rnd(a, bq, cq, AV_ROUND_NEAR_INF); +} + +int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b) +{ + int64_t a = tb_a.num * (int64_t)tb_b.den; + int64_t b = tb_b.num * (int64_t)tb_a.den; + if ((FFABS64U(ts_a)|a|FFABS64U(ts_b)|b) <= INT_MAX) + return (ts_a*a > ts_b*b) - (ts_a*a < ts_b*b); + if (av_rescale_rnd(ts_a, a, b, AV_ROUND_DOWN) < ts_b) + return -1; + if (av_rescale_rnd(ts_b, b, a, AV_ROUND_DOWN) < ts_a) + return 1; + return 0; +} + +int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod) +{ + int64_t c = (a - b) & (mod - 1); + if (c > (mod >> 1)) + c -= mod; + return c; +} + +int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts, AVRational fs_tb, int duration, int64_t *last, AVRational out_tb){ + int64_t a, b, this; + + av_assert0(in_ts != AV_NOPTS_VALUE); + av_assert0(duration >= 0); + + if (*last == AV_NOPTS_VALUE || !duration || in_tb.num*(int64_t)out_tb.den <= out_tb.num*(int64_t)in_tb.den) { +simple_round: + *last = av_rescale_q(in_ts, in_tb, fs_tb) + duration; + return av_rescale_q(in_ts, in_tb, out_tb); + } + + a = av_rescale_q_rnd(2*in_ts-1, in_tb, fs_tb, AV_ROUND_DOWN) >>1; + b = (av_rescale_q_rnd(2*in_ts+1, in_tb, fs_tb, AV_ROUND_UP )+1)>>1; + if (*last < 2*a - b || *last > 2*b - a) + goto simple_round; + + this = av_clip64(*last, a, b); + *last = this + duration; + + return av_rescale_q(this, fs_tb, out_tb); +} + +int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc) +{ + int64_t m, d; + + if (inc != 1) + inc_tb = av_mul_q(inc_tb, (AVRational) {inc, 1}); + + m = inc_tb.num * (int64_t)ts_tb.den; + d = inc_tb.den * (int64_t)ts_tb.num; + + if (m % d == 0 && ts <= INT64_MAX - m / d) + return ts + m / d; + if (m < d) + return ts; + + { + int64_t old = av_rescale_q(ts, ts_tb, inc_tb); + int64_t old_ts = av_rescale_q(old, inc_tb, ts_tb); + + if (old == INT64_MAX || old == AV_NOPTS_VALUE || old_ts == AV_NOPTS_VALUE) + return ts; + + return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts); + } +} + +static inline double eval_poly(const double *coeff, int size, double x) { + double sum = coeff[size-1]; + int i; + for (i = size-2; i >= 0; --i) { + sum *= x; + sum += coeff[i]; + } + return sum; +} + +/** + * 0th order modified bessel function of the first kind. + * Algorithm taken from the Boost project, source: + * https://searchcode.com/codesearch/view/14918379/ + * Use, modification and distribution are subject to the + * Boost Software License, Version 1.0 (see notice below). + * Boost Software License - Version 1.0 - August 17th, 2003 +Permission is hereby granted, free of charge, to any person or organization +obtaining a copy of the software and accompanying documentation covered by +this license (the "Software") to use, reproduce, display, distribute, +execute, and transmit the Software, and to prepare derivative works of the +Software, and to permit third-parties to whom the Software is furnished to +do so, all subject to the following: + +The copyright notices in the Software and this entire statement, including +the above license grant, this restriction and the following disclaimer, +must be included in all copies of the Software, in whole or in part, and +all derivative works of the Software, unless such copies or derivative +works are solely in the form of machine-executable object code generated by +a source language processor. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT +SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE +FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, +ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +DEALINGS IN THE SOFTWARE. + */ + +double av_bessel_i0(double x) { +// Modified Bessel function of the first kind of order zero +// minimax rational approximations on intervals, see +// Blair and Edwards, Chalk River Report AECL-4928, 1974 + static const double p1[] = { + -2.2335582639474375249e+15, + -5.5050369673018427753e+14, + -3.2940087627407749166e+13, + -8.4925101247114157499e+11, + -1.1912746104985237192e+10, + -1.0313066708737980747e+08, + -5.9545626019847898221e+05, + -2.4125195876041896775e+03, + -7.0935347449210549190e+00, + -1.5453977791786851041e-02, + -2.5172644670688975051e-05, + -3.0517226450451067446e-08, + -2.6843448573468483278e-11, + -1.5982226675653184646e-14, + -5.2487866627945699800e-18, + }; + static const double q1[] = { + -2.2335582639474375245e+15, + 7.8858692566751002988e+12, + -1.2207067397808979846e+10, + 1.0377081058062166144e+07, + -4.8527560179962773045e+03, + 1.0, + }; + static const double p2[] = { + -2.2210262233306573296e-04, + 1.3067392038106924055e-02, + -4.4700805721174453923e-01, + 5.5674518371240761397e+00, + -2.3517945679239481621e+01, + 3.1611322818701131207e+01, + -9.6090021968656180000e+00, + }; + static const double q2[] = { + -5.5194330231005480228e-04, + 3.2547697594819615062e-02, + -1.1151759188741312645e+00, + 1.3982595353892851542e+01, + -6.0228002066743340583e+01, + 8.5539563258012929600e+01, + -3.1446690275135491500e+01, + 1.0, + }; + double y, r, factor; + if (x == 0) + return 1.0; + x = fabs(x); + if (x <= 15) { + y = x * x; + return eval_poly(p1, FF_ARRAY_ELEMS(p1), y) / eval_poly(q1, FF_ARRAY_ELEMS(q1), y); + } + else { + y = 1 / x - 1.0 / 15; + r = eval_poly(p2, FF_ARRAY_ELEMS(p2), y) / eval_poly(q2, FF_ARRAY_ELEMS(q2), y); + factor = exp(x) / sqrt(x); + return factor * r; + } +} |